The Four Lucky Ones

There are just four numbers (after 1) which are the sums of the cubes of their digits:

153 = 1^3 + 5^3 + 3^3

370 = 3^3 + 7^3 + 0^3

371 = 3^3 + 7^3 + 1^3

407 = 4^3 + 0^3 + 7^3  [ ^ means raised to power]

Easy 9

It is easy to figure out whether a number is exactly divisible by 9. It’s similar to as asking whether a number is in the “9’s table”. You need to sum up its digits. If the answer attained is more than one digit long, then you can add up the digits again, and continue doing this, until you a single digit is what is left. If the single digit attained is 9 then the original number was divisible by 9.